Symmetry-adapted perturbation theory of nonadditive three-body interactions in van der Waals molecules. I. General theory

Symmetry-adapted perturbation theory of pairwise nonadditive interactions in trimers is formulated, and pure three-body polarization and exchange components are explicitly separated out. It is shown that the three-body polarization contributions through the third order of perturbation theory naturally separate into terms describing the pure induction, mixed induction–dispersion, and pure dispersion interactions. Working equations for these components in terms of molecular integrals and linear and quadratic response functions are derived. These formulas have a clear, partly classical, partly quantum mechanical, physical interpretation. The asymptotic expressions for the second- and third-order three-body polarization contributions through the multipole moments and (hyper)polarizabilities of the isolated monomers are reported. Finally, assuming the random phase approximation for the response functions, explicit orbital formulas for the three-body polarization terms are derived. The exchange terms are also classified, and the simplest approximations (neglecting intramonomer correlation effects) are written as explicitly connected commutator expressions involving second-quantized operators. The corresponding orbital formulas are also reported.

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